Abstract
I HAVE recently obtained the solution of this problem: Given n linear equations of condition in m unknowns, and that (1) the set of errors of the equations of condition are a sample drawn at random from a normal population of unknown standard deviation, and that (2) nothing more is known about the values of the unknowns or of than that which can be inferred from the equations of condition, then (A) what are the values of the unknowns—By rigorous, direct methods, and with no further assumptions, I have obtained the distribution functions in answer to question (A). They are the same as those which Jeffreys1 obtained in semi-intuitive fashion, by making the somewhat arbitrary assumption that the “prior probability” that lies in a certain range d is proportional simply to d/.
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References
Jeffreys, Proc. Roy. Soc., A, 138, 48; 1932.
Fisher, Proc. Roy. Soc., A, 139, 343; 1933.
Bartlett, Proc. Roy. Soc., A, 141, 518; 1933.
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STERNE, T. Accuracy of Least Squares Solutions. Nature 134, 421 (1934). https://doi.org/10.1038/134421a0
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DOI: https://doi.org/10.1038/134421a0
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